Big Idea:
students apply and interpret bar models to calculate sale prices and total costs after tax/tip

Students enter silently according to the Daily Entrance Routine. Their Do Now assignment is faced down, and students are asked NOT to turn the paper over. They must write their names on the back side of this paper without turning it over. As we continue working within this percents unit, we also continue to start class with conversion sprints. These sprints are built from materials available on the EngageNY state website developed to support the common core curriculum. For more resources within this module (Percent and Proportional Relationships) visit this link.

Students have 5 minutes to complete as many problems as possible. To continue motivating all students I continue to stagger the awards given so that students have incremental goals. Achievement points are awarded as follows:

1 achievement point if they completed an entire column

2 achievement points if they completed an entire column and 80% or more of the answers were correct

3 achievement points if they completed BOTH columns AND 80% of the answers of more were correct

4 achievement points if they completed BOTH columns and ALL of the answers were correct

This strategy worked best because it challenges students at different levels. Even the students who struggled academically the most with these conversions pushed themselves to complete an entire column and see progress. In the last 4 – 5 minutes of this section, I elect a a student to cold call the rest to give the answers and write them on the board while I am walking around awarding achievement points to students. Students are then asked to put their sprints away after all answers are reviewed and class notes are distributed.

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Resources

Students must first fill out the heading and copy the aim at the top of their notes. The class notes resources I have attached in this section also include a teacher copy of the notes. Any red fonts indicate notes that are to be written on the board for students to copy. I begin by defining sale price as “the price of a good or service that is being offered at a discount”. I give students one quick example:

Ms. Chavira wants to buy a $50 shirt. She comes back to buy it when it is on sale for $15 off. What is the sale price?

I purposefully introduce students to the term “sale price” separately from a word problem that includes a percent. Step by step.

The next topic I ask students to write on the left hand margin is “Bar Models: Discount”. Students must copy the bar model I have displayed on the board. The following key ideas must be reviewed and copied into notes around the bar model:

Point out which part of the bar model represents the discount alone

What does the entire bar represent? Original price

As a percent? The entire bar is 100% of the original price

Next, students copy the topic “Bar Models: Tax, tip, gratuities” and draw the bar model with a dotted line extension to represent the tax. The following key ideas must be reviewed and copied into notes around the bar model:

Point out which part of the bar model represents the tax/tip alone

Point out which part of the bar model represents the original price alone

What does the entire bar, included the dotted line part, represent? The total, including tax/tip

As a percent? The solid-lined rectangle is 100% of the original price; the entire rectangle, including the dotted piece, represent (100 + x)%, where x represents the percent tax/tip.

If you want to calculate the total price when considering tip/tax you can solve one of two ways:

Calculate the tax/tip and add it to the original amount

Calculate (100 + x)% of the original price to find the total

Finally, and very importantly: Tax is always applied to the sale price, NOT the original price.

This idea has implications for calculations when given multi-step problems. A common misconception to look out for is students who combine the discount with the tax and calculate the resulting percent of the original price. The lesson on successive percents will dive more in depth of this topic. [link to lesson 117]

Next, students have 6-8 minutes to work with partners to answer the two questions at the bottom of their notes. This word problem summarizes the concepts we reviewed. I ask a pair of students to show the work on the board. At the end of this section I ask all students to review the board and check their answers. They can ask questions during the independent practice section.

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Students receive class work. A timer is set for 6-7 minutes. I let them know that I will be giving them some choice about the group they can work with today, that booth seats will be available, and that the first thing they must do is complete the two problems at the top of their paper within 6 -7 minutes, with work and bar models shown. When they have completed these two problems they may raise their hands so that I can come check their work. Students who appear to understand the process and are showing good work, will be allowed to choose one of three available booths. At the end of the allotted time I will have a good idea of the group of students who should be working with me most of the time. All others will be allowed to choose groups of 4 to join and complete the task. A 10 minute timer will be displayed. At the end of this time, students must return to their seats to review the answers.

I’ll be dividing my time partly among a small group of 6 – 8 students, helping them with the Task assignment. I’m also going to prepare them with ideas and strategies I will call on them to share during the closing section of class. Once there are 3 - 4 minutes left I will return to those students who seemed to understand the process and ask them to put their work on the board.

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Resources

In the last 10 minutes of class I will be asking students to explain the solutions they displayed on the board. I will also have a document camera set up to share responses we came up with together in my small group. Since I’ve prepared them with the ideas and strategies they’ll be sharing, it should allow them to shine in ways they may not always be able to.

Any work not completed during class should be completed for homework. Answers will be posted on the class website.